Modelling particle collisions in moderately dense curtain impacted by an incident shock wave

The interactions between an incident shock and moderately dense particle curtain are simulated with the Eulerian-Lagrangian method. A customized solver based on OpenFOAM is extended with an improved drag model and collision model, and then validated against two benchmark experiments. In this work, parametric studies are performed considering different particle sizes, volume fractions, and curtain thicknesses. It is found that smaller particle size and larger volume fractions lead to stronger reflected shock and weaker transmitted shock. Different expansion stages of the curtain fronts are also studied in detail. Attention is paid to the particle collision effects on the curtain evolution behaviours. According to our results, for the mono-dispersed particle curtain, the collision effects on curtain front behaviors are small, even when the initial particle volume fraction is as high as 20%. This is due to the positive velocity gradient across the curtain after the shock wave passage, leading to faster motion of downstream particles than the upstream ones and hence no collision occurs. For the bi-dispersed particle curtain, the collision effects become important in the mixing region of different-size particles. Collisions decelerate small particles while accelerate large ones and cause velocity scattering. Moreover, increasing the bi-dispersed curtain thickness leads to multiple collision force peaks due to the local particle accumulations, which is the result of the delayed separation of different particle groups. Our results indicate that the collision model may be unnecessary to predict curtain fronts in mono-dispersed particles, but in bi-dispersed particles, the collision effects are important and therefore must be modelled.